Oscillation Theory for Neutral Differential Equations with Delay: 1st Edition (Hardback) book cover

Oscillation Theory for Neutral Differential Equations with Delay

1st Edition

By D.D Bainov, D.P Mishev

CRC Press

288 pages

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Hardback: 9780750301428
pub: 1991-01-01
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Description

With neutral differential equations, any lack of smoothness in initial conditions is not damped and so they have proven to be difficult to solve. Until now, there has been little information to help with this problem.

Oscillation Theory for Neutral Differential Equations with Delay fills a vacuum in qualitative theory of functional differential equations of neutral type. With much of the presented material previously unavailable outside Eastern Europe, this authoritative book provides a stimulus to research the oscillatory and asymptotic properties of these equations. It examines equations of first, second, and higher orders as well as the asymptotic behavior for tending toward infinity. These results are then generalized for partial differential equations of neutral type. The book also describes the historical development of the field and discusses applications in mathematical models of processes and phenomena in physics, electrical control and engineering, physical chemistry, and mathematical biology.

This book is an important tool not only for mathematicians, but also for specialists in many fields including physicists, engineers, and biologists. It may be used as a graduate-level textbook or as a reference book for a wide range of subjects, from radiophysics to electrical and control engineering to biological science.

Table of Contents

PREFACE

NOTATION

INTRODUCTION

Preliminary notes

Auxiliary assertions

FIRST ORDER NEUTRAL ORDINARY DIFFERENTIAL EQUATIONS

First order linear differential equations

First order differential equations with constant coefficients

First order differential equations with distributed delay

First order nonlinear differential equations

Oscillation and comparison of results in neutral differential equations and their applications to the delay logistic equation

Notes and comments to chapter 2

SECOND ORDER NEUTRAL ORDINARY DIFFERENTIAL EQUATIONS

Second order linear differential equations

Second order differential equations with constant coefficients

Second order differential equations with distributed delay

Second order nonlinear differential equations

Distribution of the zeros of the solutions of neutral differential equations

Notes and comments to chapter 3

NTH ORDER NEUTRAL ORDINARY DIFFERENTIAL EQUATIONS

nth order linear differential equations

nth order differential equations with constant coefficients

nth order nonlinear differential equations

Notes and comments to chapter 4

SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE

Linear systems of ordinary differential equations with constant coefficients

Notes and comments to chapter 5

NEUTRAL PARTIAL DIFFERENTIAL EQUATIONS

Linear parabolic differential equations

Nonlinear parabolic differential equations

Parabolic differential equations with "maxima"

Linear hyperbolic differential equations

Nonlinear hyperbolic differential equations

Hyperbolic differential equations with "maxima"

Notes and comments to chapter 6

REFERENCES

INDEX

Subject Categories

BISAC Subject Codes/Headings:
MAT007000
MATHEMATICS / Differential Equations
SCI040000
SCIENCE / Mathematical Physics